#6812: Enumerate integer vectors modulo to the action of a Permutation Group
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Reporter: nborie |
Owner: nborie
Type: enhancement |
Status: needs_review
Priority: major |
Milestone: sage-5.1
Component: combinatorics |
Resolution:
Keywords: enumeration, integer, list, permutation, group | Work
issues: long time tests, information about listing infinite sets
Report Upstream: N/A |
Reviewers: Karl-Dieter Crisman, Simon King
Authors: Nicolas Borie | Merged
in:
Dependencies: |
Stopgaps:
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Comment (by nborie):
I just added two files providing a good k-test (especially for invariant
theory):
The function to use is: TEST_generation_orbit_sum
The function is in the file: benchmarks_generating_orbit_sum.py
The good tests to run are the following (depending the size you want to
test):
* TEST_generation_orbit_sum(TransitiveGroup(8,1), verbose=True) (~2 sec)
* TEST_generation_orbit_sum(TransitiveGroup(9,1), verbose=True) (~20 sec)
* TEST_generation_orbit_sum(TransitiveGroup(10,1), verbose=True) (~3 min)
All the complexity are contained in such examples.
For graphs lovers and the change from list to set, you should use a test
including vector with large automorphism group like :
{{{
sage: G = TransitiveGroup(15,28)
sage: S = IntegerVectorsModPermutationGroup(G, max_part=1)
sage: timeit('S._cardinality_from_iterator()')
5 loops, best of 3: 1.3 s per loop
}}}
This test build the 156 graphs over 6 vertices enumerated up to an
isomorphism. And vectors whose entries are 0 or 1 have 'often' large
automorphism group.
Comparing the old implementation with Python list (and 2 years of
development of Sage), the module is currently 3 or 4 times faster.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6812#comment:77>
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